feat: wire frontend pages to live APIs and standardize response contracts (P1)

- Backend: Add COUNT query and paginated response shape to conversations endpoint
  Returns { conversations: [...], total, page, per_page } instead of flat array
- Frontend: Replace mock data in DashboardPage with fetchAnalytics() API calls
- Frontend: Replace mock data in ReplayListPage with fetchConversations() API calls
- Frontend: Replace mock data in ReplayPage with fetchReplay() API calls
- Add proper loading, empty, and error states to all three pages
- Align ConversationSummary type with actual DB columns (created_at, status)
- Update unit and E2E tests for new paginated conversation response shape
- Add fetchone() to FakeCursor for COUNT query support in E2E tests

backend/tests/e2e/conftest.py

@@ -107,6 +107,9 @@ class FakeCursor:
     async def fetchall(self) -> list[dict]:
         return self._rows
 
+    async def fetchone(self) -> tuple | dict | None:
+        return self._rows[0] if self._rows else None
+
 
 class FakeConnection:
     """Fake async connection that returns a FakeCursor."""